周期函数的数值微分问题  

Numerical Differentiation for Periodic Functions and Its Applications

作　　者：杨古帆[1] 叶予璋[1] 王盛章[2] 

机构地区：[1]复旦大学数学研究所,上海200433 [2]北海道大学数学系,日本扎幌0600810

出　　处：《复旦学报（自然科学版）》2004年第3期315-322,共8页Journal of Fudan University：Natural Science

摘　　要：用Tikhonov正则化方法讨论了周期函数的数值微分问题 .证明Tikhonov正则化泛函存在唯一的极小元 ,且这个极小元是一个周期样条 ,并给出了该方法的误差估计 .同其他相关的工作相比 ,发现对周期函数而言 。The numerical differentiation for the periodic functions is discussed by Tikhonov redularization. It is shown that there exists a unique minimizer for the Tikhonov regularization functional and minimizer is a periodic spline. The error estimate of our method is also given. Compared with other related methods, it gives better approximation on the boundary points. one numerical example is presented .

关 键 词：周期函数 数值微分 TIKHONOV正则化 误差估计 周期样条 变分法 

分 类 号：O241.4[理学—计算数学]